This section is intended to introduce the reader to various aspects of the art that may be related to various aspects of the present invention. The following discussion is intended to provide information to facilitate a better understanding of the present invention. Accordingly, it should be understood that statements in the following discussion are to be read in this light, and not as admissions of prior art.
The petroleum industry typically employs turbine and ultrasonic meters, for example, to measure flow rate and other fluid characteristics. The accuracy of such meters generally depends on the continuity and stability of the axial fluid velocity profiles to which they are subjected. Spatially discontinuous profiles or profiles that vary widely in time lead to unpredictable and hence unacceptable variations in the calibrations of such meters, for instance.
The axial velocity profile associated with a flowing fluid in a fully closed conduit, like a pipe, depends on the relative magnitudes of the forces acting on the fluid, which can be generally classified as either inertial forces or frictional forces. The inertial forces tend to keep fluid particles moving at a constant velocity in a constant direction, while the frictional forces between adjacent flow streams, characterized by the fluid viscosity, tend to slow the fluid down. In some instances, fluid viscosity may slow the flow rate to zero at the pipe wall. The ratio of the inertial forces to the viscous forces, which is known as the Reynolds number and is dimensionless, is often used in fluid dynamics to characterize velocity profiles.
In many industrial applications the inertial forces dominate. In such cases, the Reynolds number exceeds 5000 and the fluid flow is characterized as “turbulent”. The momentum of parallel flow streams is freely exchanged by small, random eddies; and the profile, while varying only to a small degree both spatially and temporally, is, on average, blunt, stable, and readily and accurately measured by both turbine meters and ultrasonic meters. However, in recent years, applications have required the measurement of the flows of very heavy crude oils, where Reynolds numbers are in the 500 to 5000 range and where viscous forces play an important role in determining the character of the profile. At Reynolds numbers below about 1000, the flow regime is characterized as “laminar”; in long straight pipes the velocity profile approaches a parabolic shape, but in any case, it is extremely stable and without eddies. Temperature gradients can create measurement problems in this regime but, with an isothermal product, flow measurement with ultrasonic instruments presents no insuperable problems. The use of turbine meters in this regime is more problematic however, because of the interaction of the turbine itself with the flowing fluid.
At Reynolds numbers above 1000 but below 5000, the flow regime is characterized as “transitional”. In this range, the flow may tend to be laminar, but small disturbances in fluid velocity, in the topography of the pipe wall, or the physical configuration of the measurement instruments themselves may trigger large vortices accompanied by sudden and dramatic changes in axial profile. Reference texts describe transitional flow as being like laminar flow that is interspersed with turbulent ‘puffs’ and ‘slugs’, the existence and frequency of which are dependent on the Reynolds number and other characteristics of the pipe (geometry, vibration, etc.). The time-averaged velocity profile before the puff or slug is essentially the same as a laminar profile, and in the center of the puff or slug it is essentially the same as a turbulent profile. At the leading and trailing edges of the puff or slug the profile changes from one shape to the other, and this change is accompanied by the generation of large eddies.
Neither turbine meters nor ultrasonic meters have performed acceptably in the transition region, their calibrations being too difficult to establish and too variable to be used in petroleum applications requiring accuracy, such as custody transfer and product allocation. At the present time the only instruments suited for use in the transition region are positive displacement meters, which are expensive and require frequent maintenance. The present invention provides a technique whereby ultrasonic meters may be made to operate stably and reliably in the transition region, without compromising their performance in the laminar regime below or in the turbulent regime above.
To the best of the inventors' knowledge, there is no prior application for the specific purpose measuring a velocity profile in the transition regime with an ultrasonic meter. Prior-art nozzles used for the measurement of mass flow—such as a so-called ASME nozzle—with differential pressure instruments have a bluff entry and are often characterized by a single ellipsoid as opposed to the compound cubic or compound ellipsoid used by the invention described herein. FIG. 5 illustrates a typical conventional flow nozzle profile.